For a large heterogeneous group of patients, we analyse probabilities of hospital admission and distributional properties of lengths of hospital stay conditional on individual determinants. Bayesian structured additive regression models for zero-inflated and overdispersed count data are employed. In addition, the framework is extended towards hurdle specifications, providing an alternative approach to cover particularly large frequencies of zero quotes in count data. As a specific merit, the model class considered embeds linear and nonlinear effects of covariates on all distribution parameters. Linear effects indicate that the quantity and severity of prior illness are positively correlated with the risk of hospital admission, while medical prevention (in the form of general practice visits) and rehabilitation reduce the expected length of future hospital stays. Flexible nonlinear response patterns are diagnosed for age and an indicator of a patients' socioeconomic status. We find that social deprivation exhibits a positive impact on the risk of admission and a negative effect on the expected length of future hospital stays of admitted patients.